Problem: Express your answer as a mixed number simplified to lowest terms. $4\dfrac{1}{5}-1\dfrac{2}{4} = {?}$
Solution: Simplify each fraction. $= {4\dfrac{1}{5}} - {1\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {4\dfrac{2}{10}}-{1\dfrac{5}{10}}$ Convert ${4\dfrac{2}{10}}$ to ${3 + \dfrac{10}{10} + \dfrac{2}{10}}$ So the problem becomes: ${3\dfrac{12}{10}}-{1\dfrac{5}{10}}$ Separate the whole numbers from the fractional parts: $= {3} + {\dfrac{12}{10}} - {1} - {\dfrac{5}{10}}$ Bring the whole numbers together and the fractions together: $= {3} - {1} + {\dfrac{12}{10}} - {\dfrac{5}{10}}$ Subtract the whole numbers: $=2 + {\dfrac{12}{10}} - {\dfrac{5}{10}}$ Subtract the fractions: $= 2+\dfrac{7}{10}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{7}{10}$